Create dimensionality_reduction.md

Author: matthewcso

dimensionality_reduction.md

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+## Dealing with massive image files
+
+### If a single image can fit into GPU memory
+- Use distributed processing to load 1 image on each GPU, use multiple GPUs (at least, TensorFlow supports this). [link](https://www.tensorflow.org/guide/distributed_training)
+- Fit an autoencoder and train using the internal representation.
+   - Potentially interesting if a single image modality fits, but not all 4 at once
+   - I tried this before and it didn't take that long even with batch size=1
+- Use early strided convolution layers to reduce dimensionality. Used in U-net. [link](https://arxiv.org/abs/1505.04597)
+- Image fusion
+   - principal component analysis (this also works for image compression if you do it differently)
+   - frequency-domain image fusion such as various shearlet transforms (I don't understand these, but here's a paper [link](https://journals.sagepub.com/doi/full/10.1177/1748301817741001))
+   - I guess you could probably also use an autoencoder for this
+   - This should reduce our 4-channel (4 neuroimaging types) image to have less channels containing the same information
+
+### Works even if a single image can't fit into GPU memory
+- Cropping
+    - This probably works better if the images are registered to approximately the same space
+- Slicing [Cameron's review with some of these](https://www.sciencedirect.com/science/article/pii/S187705091632587X)
+    - Use 2-dimensional slices of 3D image, which each definitely fit in memory
+    - (probably) can train models for each modality separately and average/use a less-GPU intensive model to combine them?
+    - (probably) split image into smaller 3D patches for segmentation
+- Downsampling: [this paper](https://nvlpubs.nist.gov/nistpubs/ir/2013/NIST.IR.7839.pdf) is not about neuroimaging at all but maybe has some insights?
+    - Spectral truncation
+        - Compute fast Fourier transform, reduce sampling rate, compute inverse FFT
+        - I'm going to add wavelet transform here for similar reasons
+    - Average pooling (take the average of 2x2x2 voxels)
+    - Max pooling (take the maximum of 2x2x2 voxels)
+    - Decimation/Gaussian blur with decimation (take every other line)
+- Use a convolutional neural network that works on spectrally compressed images [link](https://www.sciencedirect.com/science/article/abs/pii/S0925231219310148)
+    - probably really stupid
+    - compute FFT, discrete cosine transform, or whatever
+    - clip the spectrum to get rid of irrelevant high frequency noise
+    - use a spectral convolutional neural network to compute everything in frequency domain
+    - transform back to image domain 
+